A097024 Numbers in the 5-cycle-attractor of the function f(x)=A063919(x).

1482, 1878, 1890, 2142, 2178

Offset: 1

Author

Labos Elemer, Aug 30 2004

Keywords

• nonn
• more

Comments

A002827 provides 1-cycle terms = unitary perfect numbers.

A063991 gives 2-cycle elements = unitary amicable numbers.

A097030 collects true 14-cycle elements, i.e., terms in end-cycle of length 14 when A063919(x) function is iterated.

Concerning 3-cycle elements, only {30,42,54} were encountered.

Links

• J. O. M. Pedersen, Order 5 cycles, 2007.

Crossrefs

Cf. A063919, A002827, A063991, A097030.

Programs

Mathematica

a063919[1] = 1; (* function a[] in A063919 by Jean-François Alcover *)
a063919[n_] := Total[Select[Divisors[n], GCD[#, n/#]==1&]]-n/;n>1
a097024Q[k_] := Module[{a=NestList[a063919, k, 5]}, Count[a, k]==2&&Last[a]==k]
a097024[n_] := Select[Range[n], a097024Q]
a097024[2178] (* Hartmut F. W. Hoft, Jan 24 2024 *)

PARI

f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;
isok5(n) = iferr(f(f(f(f(f(n))))) == n, E, 0);
isok1(n) = iferr(f(n) == n, E, 0);
isok(n) = !isok1(n) && isok5(n); \\ Michel Marcus, Sep 28 2018